Details

sample28.0ms

Algorithm

intervals

Results

8.0ms	195×	body	80	valid
4.0ms	29×	body	640	valid
1.0ms	14×	body	320	valid
1.0ms	8×	body	1280	valid
1.0ms	10×	body	160	valid

simplify4.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	16	11
2	35	11
3	74	11
4	123	11
5	210	11
6	232	11
7	248	11
8	275	11
9	327	11
10	346	11
11	352	11
12	367	11
13	383	11
14	470	11
15	561	11
16	816	11
17	1118	11
18	1527	11
19	1608	11
done	1608	11

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
1.8b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
8.9b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
10×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt`
5×	`pow1` `associate-l` `add-log-exp`
4×	`times-frac` `associate-l/` `associate-/r`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `associate-/l/` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `frac-2neg` `flip3-+` `diff-log` `pow-prod-down` `clear-num` `-commutative` `flip-+` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 63

Calls

3 calls:

38.0ms	(* (- 1.0 x) y)
41.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
24.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series201.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(* (- 1.0 x) y)
88.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
70.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify1.5s

Counts

72 → 72

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	128	885
1	335	828
2	1274	746
done	5001	744

prune180.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (+ y 1.0))
0.0b	(* (- 1.0 x) (/ y (+ y 1.0)))
1.8b	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
25×	`times-frac`
21×	`add-cube-cbrt`
18×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
7×	`distribute-lft-out`
5×	`pow1` `associate-l` `add-log-exp`
4×	`associate-/r*` `associate-/r/`
3×	`flip3--` `flip--` `associate-/l*`
2×	`cbrt-undiv` `frac-times` `flip3-+` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 88

Calls

3 calls:

13.0ms	(/ y (+ y 1.0))
60.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
8.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

series198.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ y (+ y 1.0))
57.0ms	(* (- 1.0 x) (/ y (+ y 1.0)))
94.0ms	(- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))

simplify1.6s

Counts

97 → 97

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	157	1229
1	395	1148
2	1387	1056
done	5000	1054

prune234.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize40.0ms

Local error

Found 4 expressions with local error:

8.9b	(/ (* (- 1.0 x) y) (+ y 1.0))
8.9b	(/ (* (- 1.0 x) y) (+ y 1.0))
8.9b	(/ (* (- 1.0 x) y) (+ y 1.0))
10.4b	(/ (- (* 1.0 1.0) (* (/ (* (- 1.0 x) y) (+ y 1.0)) (/ (* (- 1.0 x) y) (+ y 1.0)))) (+ 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
28×	`times-frac`
21×	`add-exp-log` `add-cbrt-cube`
20×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`associate-/r*`
11×	`distribute-lft-out`
8×	`associate-/r/` `associate-/l/`
7×	`cbrt-undiv` `div-exp` `associate-/l*`
6×	`associate-*l/`
5×	`difference-of-squares`
4×	`pow1` `flip3--` `frac-2neg` `flip3-+` `clear-num` `flip--` `flip-+` `div-inv` `add-log-exp`
3×	`prod-exp` `cbrt-unprod`
1×	`div-sub`

Counts

4 → 122

Calls

4 calls:

24.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
37.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
24.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
83.0ms	(/ (- (* 1.0 1.0) (* (/ (* (- 1.0 x) y) (+ y 1.0)) (/ (* (- 1.0 x) y) (+ y 1.0)))) (+ 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))))

series837.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
56.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
67.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
659.0ms	(/ (- (* 1.0 1.0) (* (/ (* (- 1.0 x) y) (+ y 1.0)) (/ (* (- 1.0 x) y) (+ y 1.0)))) (+ 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))))

simplify1.1s

Counts

134 → 134

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	153	3329
1	429	3135
2	1602	2867
done	5000	2581

prune447.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize26.0ms

Local error

Found 4 expressions with local error:

8.9b	(/ (* (- 1.0 x) y) (+ y 1.0))
8.9b	(/ (* (- 1.0 x) y) (+ y 1.0))
8.9b	(/ (- (* (- 1.0 x) y)) (- (+ y 1.0)))
10.4b	(/ (- (* 1.0 1.0) (* (/ (- (* (- 1.0 x) y)) (- (+ y 1.0))) (/ (* (- 1.0 x) y) (+ y 1.0)))) (+ 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

95×	`*-un-lft-identity`
92×	`times-frac`
51×	`add-sqr-sqrt` `add-cube-cbrt`
41×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
24×	`associate-/r*`
22×	`distribute-lft-out`
20×	`neg-mul-1`
18×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/l*`
8×	`associate-/r/` `associate-/l/`
6×	`cbrt-undiv` `div-exp` `associate-*l/`
4×	`pow1` `flip3--` `frac-2neg` `flip3-+` `clear-num` `flip--` `flip-+` `div-inv` `distribute-neg-frac` `add-log-exp`
2×	`div-sub` `prod-exp` `cbrt-unprod`
1×	`neg-sub0` `distribute-frac-neg`

Counts

4 → 198

Calls

4 calls:

33.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
25.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
41.0ms	(/ (- (* (- 1.0 x) y)) (- (+ y 1.0)))
93.0ms	(/ (- (* 1.0 1.0) (* (/ (- (* (- 1.0 x) y)) (- (+ y 1.0))) (/ (* (- 1.0 x) y) (+ y 1.0)))) (+ 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))))

series823.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
65.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
70.0ms	(/ (- (* (- 1.0 x) y)) (- (+ y 1.0)))
620.0ms	(/ (- (* 1.0 1.0) (* (/ (- (* (- 1.0 x) y)) (- (+ y 1.0))) (/ (* (- 1.0 x) y) (+ y 1.0)))) (+ 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))))

simplify1.7s

Counts

210 → 210

Iterations

Useful iterations: 2 (535.0ms)

Iter	Nodes	Cost
0	288	4812
1	723	4615
2	2668	4286
done	5000	4286

prune672.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

regimes135.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 14.2b

bsearch115.0ms

Steps

Iters	Range		Point
9	137362616.0762091	1439059428709982.0	512264646.35448426
7	-2445851338.3862987	-30461436.183609415	-118579514.58451813

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	19	41
1	26	31
done	26	31

end0.0ms

sample1.1s

Algorithm

intervals

Results

387.0ms	6123×	body	80	valid
243.0ms	755×	body	640	valid
86.0ms	364×	body	1280	valid
65.0ms	506×	body	320	valid
21.0ms	252×	body	160	valid